Quantum versus semiclassical description of light interaction with atomic ensembles: Revision of the Maxwell-Bloch equations and single-photon superradiance

Abstract

Interaction of atoms with quantum states of light is a long-standing problem that apart from fundamental physics has potential applications for optical quantum-state storage, quantum communication, and quantum information. A fully quantum mechanical treatment of this problem is usually very complicated mathematically. Here we show, however, that quantum mechanical evolution equations describing single-photon emission (absorption) by atomic ensembles can be written in a form equivalent to the semiclassical Maxwell-Bloch equations. This connection allows us to find exact analytical solutions of the fully quantum mechanical problem. We also found that semiclassical Maxwell-Bloch equations should be written in a form different from those commonly used. Namely, the classical limit of the quantum problem gives a propagation equation with the Laplacian operator on the right-hand side rather than with the second-order time derivative.